Level sets of depth measures in abstract spaces.

The lens depth of a point has been recently extended to general metric spaces, which is not the case for most depths. It is defined as the probability of being included in the intersection of two random balls centred at two random points and , with the same radius (, ). We prove that, on a separable and complete metric space, the level sets of the empirical lens depth based on an iid sample, converge in the Painlevé-Kuratowski sense, to its population counterpart.

Retrieving the structure of probabilistic sequences of auditory stimuli from EEG data.

Using a new probabilistic approach we model the relationship between sequences of auditory stimuli generated by stochastic chains and the electroencephalographic (EEG) data acquired while 19 participants were exposed to those stimuli. The structure of the chains generating the stimuli are characterized by rooted and labeled trees whose leaves, henceforth called contexts, represent the sequences of past stimuli governing the choice of the next stimulus. A classical conjecture claims that the brain assigns probabilistic models to samples of stimuli.

An ANOVA approach for statistical comparisons of brain networks.

The study of brain networks has developed extensively over the last couple of decades. By contrast, techniques for the statistical analysis of these networks are less developed. In this paper, we focus on the statistical comparison of brain networks in a nonparametric framework and discuss the associated detection and identification problems.

Variability in functional brain networks predicts expertise during action observation.

Observing an action performed by another individual activates, in the observer, similar circuits as those involved in the actual execution of that action. This activation is modulated by prior experience; indeed, sustained training in a particular motor domain leads to structural and functional changes in critical brain areas. Here, we capitalized on a novel graph-theory approach to electroencephalographic data (Fraiman et al.